Connecting device for wave guides



April 22, 1952 M. JOUGUET 2,594,031

' CONNECTING DEVICE FOR WAVE GUIDES Filed March 17, 1949 m ma el Bl m4 m2 9| B2 92 BI 3 e2 92 me 63 ms 62 m4 m5 FIG. 30 I FIG. 3b FIG.3C FIG. 3d

INVENTOR MARC JOUGUET ATTORNEYS Patented Apr. 22, 1952 UNITED STATES PATENT OFFICE pagnie Industrielle des Telephones, Paris,

France, a corporation of France Application March 17, 1949, Serial No. 81,897 In France April 8, 1948 2 Claims. 1

It is well-known that waves of ultra-high frequency of the so-called (Ho) or (IE) type, capable of being propagated in a circular-section wave guide, have remarkable properties which render them of great advantage in practical use, on the one hand they are little affected by the slight accidental distortions of the straight sections of the guide, and on the other hand the currents which they produce in the wall of the guide are purely transversal, so that they only undergo a slight attenuation, which is the less the higher the frequency.

On the other hand, their use involves difficulties owing to the fact that they can be transmitted only in guides with linear axis, and that, consequently, they cannot go around a bend without being at least partially transformed there into waves of the type usually called (E1) or (TMi) except for certain particular values of the angle at which the bend causes the axis of the guide to rotate, as has been explained in British Patent 643,601, published September 20, 1950.

The object of the present invention is a device for connection between two guides of circular cross section, the axes of which have different directions without restriction which make it possible to cause a wave of type (Ho) to pass, Without any perceptible loss of energy, from the first'guide to the second.

The invention will be understood by reference to the following specification and the accompanying drawings, wherein:

Fig. 1 shows a section of a curved wave guide;

Fig. 2 shows the orientation in space of the planes containing the several sections of guides whose assembly constitutes the connection device according to the present invention;

Figs. 3a, 3b, 3c, 3d, show illustrative examples of how to determine the structural elements of the device according to the present invention; and

Fig. 4 shows two sections which are straight and parallel but not colinear, connected by an s-shaped bent section.

Fig. 5 is a perspective view of a structural embodiment of the improved wave guide of circular cross section of the present invention, showing the several successive guide pieces assembled and the bends therein.

In order to give a better understanding of the present invention, it is necessary to recall some of the essential properties of the (Ho) and (E1) types of waves.

(1) Let us first of all consider the case of the propagation of these waves in a linear guide.

(a) For a given frequency, various (H0) waves many exist (the higher in number the higher the frequency) which correspond to the zeros of the Bessel function of the order one, normally designated by the notation, that is, the values of the argument for which J1=0. Hereinafter ,iLn will designate the nth non-zero root of the equation J1(Z) =0. The corresponding wave isthe wave (H0, n). All the waves (Ho) have a circular symmetry around the axis of the straight guide. The phasespeed varies with the index n.

The roots of the equation J1(Z) =0 for successive orders 1, 2, 3, 4 it (other than the root zero) are 3.8317, 7.0156, 10.1735, 13.3237, as tabulated, for instance, on page 166 of the third (1938) edition of the Jahnke and Emde Tables of Functions. In this present specification, these successive roots are designated ,ui, ,uz, ,us, 114, JLn.

(b) For a given frequency, there may also be a more or less high number of waves of type (E1) corresponding to the zeros of the equation J1(Z) =0.

The nth non-zero root of the equation that is at [.Ln, thus also corresponds to the wave (E1, n). For the same frequency, the waves (Ho, 11) and (E1, 11) have the same phase speed.

(c) For any wave (E1, n), there are two planes of symmetry passing through the axis of the straight guide. We will callthese the principal plane and the anti-principal plane. They are orthogonal and are characterised by the following properties:

(1) At any point of the principal plane, the electrical field is normal to this plane, and the magnetic field is radial, i. e. directed along the intersection line of the principal plane and the right-section plane.

(2) At any point of the anti-principal plane, the electrical field is contained in this plane and the magnetic field is normal to this plane.

In the anti-principal plane there are nodal straight lines parallel to the axis of the straight guide. At any point of these straight lines the magnetic field is nil, while the electrical field is parallel to the axis of the straight guide.

(2) Let us now consider the case of propagation through a guide of which the axis is curved.

It will be assumed that this axis of the guide is contained in a plane which will be called plane Q. If a Wave of type (E1) has its principal plane perpendicular to the plane Q, it will be said that it is a wave of type (E'i); if its principal plane coincides with the plane Q, it will be said that it is a wave of type (E1).

In such a curved guide, the waves (Ho, 11) and (E1, 11) are replaced by three waves which, for a given frequency, have slightly difierent phase speeds. These three waves are:

(a) two mixed waves which will be designated (H0, 11+E1, 11) and (H0, 11-E1, 11) the component (E1, 1;) of these waves having its principal plane merged with the plane Q. These mixed waves can also be designated by the notations (H0, n+E 'l, n) and (F10, 1|.-E"1, n).

(b) A wave (E1, 11) having its anti-principal plane merged with the plane Q; it may be called wave (E'1, 11).

' (3) Let us now examine the influence of a bend on the propagation of these waves.

When a guide with circular cross section has a bend, a wave (Ho, 11) applied at the input end of the bend generates there the two mixed waves defined above. These w'aves'are propagated at different phase speeds, and the result is that we getin general at the output end of the bend, a mixtureof wave (Ho, 11) and of wave (E1, 11) having its principal plane merged with the plane Q of the bend.

Let be the angle through which the bend causes the axis of the guideto rotate when passing from one end to the other of the bend. This angle-is shown in Fig. 1, which represents a cross section through the plane Q of the bent guide.

In the particular case in which 0, expressed in radians, is an exact integral multiple of the angle i being the wave length in free space and R the radius of the straight section of the-guide and 11 being the nth non-zero root of the equation J1(Z)=0 as above defined, we get again-entirely thewave of type (Ho, 11) at the output end of the bend.

It the angle 0 is 2. odd multiple of the bend wholly transforms the wave of type (H0, 11) into wave-of type (E" 1, n)-

Similarly, a wave of type. (E1, 11), having its principal plane merged with the plane Q, that is when applied to the input end of the guide, a wave of type (E"1, 11). is, generally speaking, transformed into a mixture of wave of type (HO n) and of wave of type (E"1, 11). If the angle 0 is an exact integral multiple ofe the wave E"1,11 alone is found again at the output of the bend. If the angle 0 is an odd multiple of radians, and, for the middle portion, a value 92 such that cos B$sin 0, sin 0 cos 6 2 cos 0 cos 1 designating the Wave length in free space and R being the radius of the straight portion of the guides and 11 being the nth non-zero root of J1(Z) =0 as above defined.

If the axes of the two guides are not co-planar, which is the general case, the angle [3 between themes of the two guides is defined in the usual manner that cos fi'equals the sum of the paired direction cosines of the two axes.

Theoperation of a device of this kind will'now be explained, by means of Figs. 2 and 3.

It will be assumed that in a linear guide G1, of which-the axis is M1M2 (Fig. 2) a wave of type (Ho, 11) is propagated. At M2 there is connected to the guide G1 a bend C1, composed of a guide with circular cross-section of which the axis is curved along an arc Mzlvls tangential-at Mz to MiMz and is situated in a plane Q1 which contains M1M2. A second'bendCz, similar to the preceding oneis connected to the bend C1. Its axis is curved along an arc M3M1 having: the same tangent at Ma as the arc M2Ma. Thisarc M3M4 is contained in a. plane Q2 perpendicular to Q1 and passing through the common tangent at M3 to the arcs 'MzMx and M3M4. At M4 a'bend C3, similar to C1'and to C2, is connected to the bend C2. Its axis, curved along the arc M4M5 has the same tangent at M4. as the arc MaM4 and it is contained in the plane Qsled by'this common tangent, perpendicular to the. plane Q2. Finally there is connected to the bend C3 alinear guide G2 at which the axisMaMs, tangential at M5 to the axis M4Ms,.iS contained in the plane Q3.

Instead of being directly connected to each other, the bends C1, C2, Ca,'may, according to. the present invention, be separated by portions of linear guides. The arcs Mzlvla, MaMi, and M4M5 may be arcs of a circle or arcs of any plane curves.

010203 will designate respectively the values which the angles defined'above (Fig; 1) assumes for the bends C1, C2 and C3.

The angle formed by the direction of the axis MsMe of the guide G2 with the direction of the axis M1M2 of the guide G1 has been designated by [3, which guides G1 and G2 are the two terminal sections of guides to be joined; 'The'value of this angle 5 is determined by the configuration of the system in which the guides are to be mounted, such as the location-of street-intersections and other obstacles, and can not be chosen arbitrarily. The value of B must'be determined before the angle 02 can befdetermined. dis the angle enclosed'between the parallels to M1M2 and M5Ms (Fig. 2) to which corresponds the angle mzoms of Fig- 3. v i

It willbe noted that the straight lines M1M11 and Mama. are-notgenerallyinthe same plane; Y

5 The angles 01 and a; are, according to the invention, odd multiples of the angle.

The angle 02 may have any value, which, as will be seen further on, can always be chosen so that the angle has a given value.

In accordance with the properties set forth above, the wave of type (Ho, n) which is propagated in guide G1 is transformed by the bend Ci into a wave of type (E1, 11) assuming the plane Q1 to be the principal plane and the plane Q2 to be the anti-principal plane. This wave of type (E1, 11) goes around the bend C2 without any great change, because it is, for this bend, a wave of type (E'i, n). For the bend C3, on the other hand, it is a wave of type (E"1, n), and this bend transforms it entirely into wave of type (Ho, n) which is then propagated in the guide G2. Thus the passage of the wave of type (Ho, n) from the guide G1 to the guide G2 has been effected.

It is easy to calculate the angle ,8 between the axes of guides G1 and G2 as a function of 0102 and 03. It is sufficient for this purpose to consider the indicatrix of the tangents as hereinafter defined to the line M1M3. In Figs. 3a., 3b, 3c, 3d, the indicatrix of the tangents is the curve which the point m describes when any point M describes the linear curve Ml-MB (Fig. 2). It is possible to choose as the positive direction of the passing between M1 and Ms that from M1 to M6. Let M be any point between M1 and Me. Through a point of the space (Fig. 3) a straight line Om is drawn parallel to the tangent at M to the line MiMa; let m be the point where this straight line intersects the sphere of center 0 and of radius equal to unity. When M passes from M1 to Me, m describes on the spherical surface the indicatrix of the tangents. The fixed point me corresponds to the straight line MIMZ- The arcs (Fig. 3) of great circles m2ms=01, m3m4=0z and mans-=03 correspond respectively to the arcs MzMa, M3M4, MiMs of Fig. 2. The fixed point me corresponds to the segment of a straight line MsMe. The angle 5 is measured by the arc of a great circle mama on the spherical surface.

There are two possible orientations for the bend C2 in the plane Q2 and two possible orientations for the bend C3 in the plane Q3.

The result is that there are four possible arrangements for the three bends, and the four in-- dicatrices of the tangents shown in Figs. 3a, 3b, 3c, 3d correspond respectively to these four arrangements. As, however, 01, 92, 03 have given values, there are only two possible values for the angle 8: Figs. 3a and 3b-give the same angle 51, and Figs. 3c and 3d the same angle 52. The classical formulae of spherical trigonometry give:

cos cl=cos 01 cos 02 cos Ha+sin 01 sin 03 cos fi2=cos 01 cos 02 cos 03Sln 01 sin 63 In practice it is the angle ,8 which is known. Thus, when the particular values given by Formulae 2 have been chosen for 01 and 03, it is possible to determine by means of Formula, 3 the value of the angle 02 of the central bend of the connecting device according to the present invention.

Thus we have:

cos SM-sin 0; sin 0}, cos cos 0; cos 0; (4)

sphere of unit radius of the indicatrix and look-- ing in the direction of the tangents. The indica-' trix sphere is the sphere of unit radius on which are traced the indicatrices of the tangents. At ms and mi it rotates through an angle of If it effects this rotation twice in the same direction (case of Figs. 3a and 3b) the sign in Formula 4 must be taken. In the contrary case (that of Figs. 3c and 3d the plus sign must be taken.

The positive or zero integral numbers K and K being chosen, Formula 4 gives '02, provided that cos 02 be comprised between -1 and +1. There is always at least one solution; there can be two.

An example will now be given, as an indication of the values assumed, in a particular case, by the angles defined by the bends of the connecting device according to the present invention.

It will be assumed that it is desired to transmit a wave (H0,1). We then have ,LLn /LI and the Formula 1 becomes:

0 R degrees It W111 also be assumed that the ratio i R is equal to 1/5; the Formula 5 then gives:

60:31 degrees If we assume K=K=0, the Formulae 2 give 01:03:15.5 degrees For 5:20, the Formula 4 gives only one solution corresponding to the sign (arrangement of Figs. 3a and 3b) 02:16.2 degrees For 8=40, it gives two solutions:

02:62.7 degrees and 02:51.5 degrees the device,.at any point whatsoever, an S-shaped.

guide such as that shown in Fig. 4. As the axis has parallel directions at the input and output of this S-shaped guide, the latter in no way interferes with the operation of the device.

What I claim is:

1. A device for connecting two rectilinear wave guides of circular cross section, said guides being such that the axis of the first guide makes an angle 5 with a line which is parallel to the axis of the second guide and which crosses the axis of the first guide, said device being so constructed that a wave of the H0 or TEo type which is being propagated in a first one of said guides passes without sensible loss of energy into the second said guide, said two wave guides being prolonged by a first length of curved guide and a second length of curved guide forming arcs the central where Mn is the nthnon zeroroot of the Bessel J1 7 function according to'the Jahnke' and Emde tables, and Xis the wave length in free space, and R- ls the" radius ofthe cross section of'the guides,

said"dvicebeing characterized'by the fact that it'- compri'se's between said first and second lengths of curved-guide, an intermediate third length of curved "guide forming an'archaving a central angle 02 such that g s sin 0 sin 0;

Q cos 0 cos 0 whose ecur ve'daxis .is situated' in a planeQz perpendicular to the planes Q1 and Q3 of the curved axes" of said first and secon'd'lengths of curved guide, sothatthe first said length transforms the Ho wave'into an E1 wave, and that the intermediate said third length of curved guide transmits the E1 Wave substantially without attenuation, and that said second length of curved guide transforms the E1 wave into a Ho wave.

2. A device for connecting two rectilinear Wave guides of circular cross-section which are adapted to convey ultra h'igh fr'equency electromagnetic wave energy. said wave guides being such that the axis of the'first guide makes an angle (3 with a line WhiCh'iS parallel .to the axis of thesecond guide and which crosses the axis of the first guide, comprising a first curved guide and a j and 03, said angles being multiples of, respective1y,-'angle's 01 and 03 which angles are add multiples of where Mn is thenth non-'zerovalue of the-Bessel function J1 and A is the wave length in freespace' of the transmitted wave, and R' is theradiusof the cross section 'of said guides, said device further comprising interposed between said first and second curved guides, an intermediate third curved: forming an arc the'central angle 02013 which is such that I t cos 6 sin 0 sin 6;

cos 6 cos 0 and whose curved axis lies in a plane Q2 perpencos 0 dicular to the planes Q1 and Q3 of the curved axes of said first and second curved guides respectively.

MARC JOUGUET.

REFERENCES CITED The following references are of record in the file of this patent:

FOREIGN PATENTS Country Date Great Britain July 15, 1947- Number 

